Quartile Calculator
Enter a dataset to find Q1, Q2 (median), Q3, interquartile range (IQR), and outlier boundaries instantly — with sorted data, box plot values, and step-by-step quartile calculation.
Enter your values above to see the results.
Tips & Notes
- ✓Always sort data before computing quartiles. Quartiles depend on the ordered positions of values — unsorted data produces completely wrong results.
- ✓Different software uses different quartile methods. Excel's QUARTILE.INC and QUARTILE.EXC give different values for the same data. This calculator uses the most common interpolation method — verify if you need to match a specific tool.
- ✓IQR is the most outlier-resistant measure of spread. A single extreme value cannot move Q1 or Q3 unless it falls inside the middle 50% — which outliers do not. Use IQR instead of range when outliers are present.
- ✓The 1.5×IQR rule for outliers is a guideline, not a law. Some fields use 3×IQR for extreme outliers. Always examine flagged outliers manually before removing them — they may be real data, not errors.
- ✓A box plot's whiskers extend to the most extreme non-outlier values, not to Q1−1.5×IQR and Q3+1.5×IQR exactly. The fence defines what counts as an outlier; the whisker stops at the last real data point within the fence.
Common Mistakes
- ✗Forgetting to sort the data before computing quartiles. Q1 is not simply the average of the first quarter of your data as entered — it depends on values in ascending order.
- ✗Confusing quartiles with percentages of the data count. Q1 is not the value at position n/4; it is the value at the 25th percentile, which may require interpolation between positions.
- ✗Using range instead of IQR for skewed data. Range uses only the minimum and maximum, making it extremely sensitive to outliers. IQR uses Q1 and Q3, covering only the middle 50% and ignoring the extremes entirely.
- ✗Thinking the 1.5×IQR rule identifies "wrong" data. Outliers are statistically unusual — not necessarily errors. A salary of $500,000 in a dataset of average salaries is an outlier but may be real and important.
- ✗Comparing IQRs from datasets with different scales. A dataset of heights in centimeters has a different IQR scale than heights in inches. Divide IQR by the median to get a scale-free spread measure.
Quartile Calculator Overview
Quartiles divide a dataset into four equal parts, each containing 25% of the values. They answer the question: where does the bottom quarter end, where does the middle half sit, and where does the top quarter begin? Quartiles form the foundation of box plots, outlier detection, and robust data summaries that resist distortion by extreme values. Unlike the mean and standard deviation, quartiles are unaffected by outliers.
Quartile definitions:
Q1 = 25th percentile | Q2 = 50th percentile (median) | Q3 = 75th percentile
EX: Sorted data [2, 5, 7, 8, 10, 13, 15, 18, 20, 24] → Q1 = average of positions 2,3 = (5+7)/2 = 6 | Q2 = (10+13)/2 = 11.5 | Q3 = (18+20)/2 = 19Interquartile range (IQR) — spread of the middle 50%:
IQR = Q3 − Q1
EX: IQR = 19 − 6 = 13 → The middle 50% of values spans a range of 13 unitsOutlier detection using the 1.5×IQR rule:
Lower fence = Q1 − 1.5×IQR | Upper fence = Q3 + 1.5×IQR
EX: Q1=6, Q3=19, IQR=13 → Lower fence = 6−19.5 = −13.5 | Upper fence = 19+19.5 = 38.5 | Any value outside [−13.5, 38.5] is a potential outlierBox plot construction — five key values:
| Value | Position | Meaning |
|---|---|---|
| Minimum | Lower whisker end | Smallest non-outlier value |
| Q1 | Box left edge | 25% of data falls below here |
| Q2 (Median) | Line inside box | Middle of the dataset |
| Q3 | Box right edge | 75% of data falls below here |
| Maximum | Upper whisker end | Largest non-outlier value |
Frequently Asked Questions
Quartiles divide a sorted dataset into four equal parts. Q1 (25th percentile) is the value where 25% of data falls below. Q2 (50th percentile) is the median — half above, half below. Q3 (75th percentile) is where 75% falls below. The interquartile range (IQR = Q3−Q1) measures the spread of the middle 50%. Together they describe the distribution without being influenced by extreme values.
The interquartile range (IQR = Q3 − Q1) measures the spread of the middle 50% of data. Unlike range or standard deviation, IQR is completely resistant to outliers. Example: data [1,2,3,4,5] has IQR=2. Adding an outlier to get [1,2,3,4,5,500] still gives IQR=2 — the outlier has no effect on Q1 or Q3. IQR is the standard spread measure for skewed data and for box plots.
Use the 1.5×IQR rule: Lower fence = Q1 − 1.5×IQR, Upper fence = Q3 + 1.5×IQR. Any value outside these fences is a potential outlier. Example: Q1=10, Q3=30, IQR=20. Lower fence = 10−30 = −20, Upper fence = 30+30 = 60. A value of 75 is an outlier; a value of −25 is also an outlier. Values between −20 and 60 are not flagged as outliers.
For odd n: split the data into lower and upper halves, each excluding the median. Q1 is the median of the lower half; Q3 is the median of the upper half. For even n: split equally. Q1 is the median of the lower half; Q3 is the median of the upper half. Example: [1,2,3,4,5,6] → lower half [1,2,3], Q1=2; upper half [4,5,6], Q3=5; IQR=3.
There are multiple methods for calculating quartiles, and different tools use different ones. The three most common are: Method 1 (exclusive) used by some textbooks, Method 2 (inclusive) used by Excel's QUARTILE.INC, and Method 3 (linear interpolation) used by R and most statistics software. For small datasets, these methods can give noticeably different results. The differences disappear as n grows large.
A box plot visualizes the five-number summary: minimum, Q1, Q2 (median), Q3, maximum. The box spans Q1 to Q3 (IQR), with a line at the median. Whiskers extend to the most extreme non-outlier values; points beyond are plotted individually as outliers. Box position shows where the data center sits; box width shows spread; median line position shows skewness; whisker length shows tail behavior.